- Email: [email protected]
A neutron spectrometer for neutrons with energies between 1 eV and 10 keV
Nuclear Instruments and Methods in Physics Research A290 (1990) 237-241 North-Holland
A NEUTRON SPECTROMETER FOR NEUTRONS WITH ENERGIES BETWEEN I eV AN
237
10 LeV
C.K. WANG * and T.E. BLUE
Ohio State University, Columbus, OH 43210, USA Received 30 Ocivber 1989
Epithermal neutrons with energies between 1 eV and 10 keV are of great interest in neutron capture therapy for treating deep-seated tumors. A new type of neutron spectrometer has been developed to measure neutron spectra :n this energy range. Conceptually, this new spectrometer is similar to the Bonner Sphere spectrometry system, in that it has a set of response functions which peak at various positions on the logarithmic energy scale. Therefore, by collecting a set of count rates, one can unfold the neutron spectrum. The performance of the spectrometer was tested in an experiment, and the associated unfolding technique was tested numerically. The results were satisfactory.
l. Introduction
Due to recent positive clinical results in Japan [1], research efforts in boron neutron capture therapy (BNCT) are regaining momentum . Among BNCT re= searchers, it is now the consensus [2] that epithermal neutron beams have advantages over thermal beams in treating deep-seated tumors, and large neutron fields have advantages over narrow neutron beams. Consequently, efforts are currently being made to extract large intense epithermal-neutron beams from nuclear reactors [3-5] and to create large intense epithermalneutron fields with accelerator-based neutron sources [6]. Radiobiological and neutronic studies have been performed which show that neutrons with energies between 1 eV and 10 keV are most suitable for treating deep-seated tumors. However, techniques for measuring epithermal-neutron spectra in large uncollimated neutron fields are not well developed. This paper describes the development and testing of a new type of neutron spectrometer for the measurement of epithermal-neutron spectra in large uncollimated neutron fields . This ribcS all Wp\rllili\ria1. nment in whiw vra ch paper 7Gr also l1G deJclaVG rllili\ria1. .m the u e muar neutron spectrum was measured for an accelerator-based neutron source for BNCT using this new spectrometer, and the measured spectrum is compared with the spectrum calculated with a Monte Carlo transport code .
* Present address: Kansas State University, Nuclear Engineering Department, Manhattan. KS 66502, USA.
2. Description of the neutron spectrometer The new neutron spectrometer is called a "boronshell spectrometer", and is similar in principle to a Bonner Sphere spectrometer. A Bonner Sphere spectrometer does not work well in this application, because: (1) it significantly modifies the neutron field at the beam port, and (2) its response functions do not show any peaks for neutron energies below 10 keV . The boron-shell spectrometer was developed to overcome these problems . As its name implies, the boron-shell spectrometer is based on a set of interchangeable hemispherical shells, which contain various amounts of '°B. A small (one inch in diameter) spherical 3 He proportional counter is a second component of the spectrometer. The proportional counter is located at the focus of the hemispherical shells (which will hereafter be called boron shells for convenience) . For the boron shells which contain larger amounts of '°B, the spectrometer has a third component, a spherical paraffin jacket which surrounds the 3He proportional counter. This jacket is matched to the boron shell, and is thicker for boron sheik which contain larger amounts of ' °B. Fig. 1 illustrates the geometric configuration of the boron-shell spectrometer. Arguments which support such a configuration are provided below : incoming neutrons are filtered by the spherical boron shell, before they reach the 3He counter. In its implementation the shell was made hemispherical, in order to conserve '°B. This was appropriate, since the neutron field which was
0168-9002/90/$03 .50 0 1990 - Elsevier Science Publishers B.V . (North-Holland)
C. K Wang, T.E. Blue/ A neutron spectrometer
238 Incident Neutrons
Void
-4
Boron Shell
{r-
1.25 cm
2.5 cm
Helium-3 Proportional Counter
Fig . 1 . The geometric configuration of the boron-shell neutron spectrometer.
measured was forwardly directed. Because the boron shell is spherical, neglecting scatter within the shell, the neutrons that strike the 3 He counter are restricted to those which are nearly perpendicularly incident upon the boron shell, and these neutrons pass through nearly 1°B the same thickness of in reaching the counter. Therefore, the filtering of spectra, and hence the response function of the spectrometer, depends only on the neutron energy (En ) and not on the neutron angular distribution . Since the neutron-capture cross section of 10B is proportional to En- 1/2, the boron shell filters out low-energy neutrons in preference to high-energy neu-
c
H
c
0 U
c
Table 1 As-built shell jacket compositions for the boron-shell neutron spectrometer Detector number
I° B loadings [g/cm2]
Paraffin thickness [cm]
1 2 3 4 5 6 7
0 .036 0 .067 0 .15 0 .39 0 .55 0 .79 0.95
0.0 0.0 0.64 0 .95 0 .95 0 .95 1 .27
trons . However, since the neutron-capture cross section for 3 He is also proportional to E. 1/2, the 3 He counter responds most strongly to the neutrons with the lowest energies . Therefore, by using a set of boron shells with various 1° Ii loadings and a 3 He counter, one can develop a set of response functions which peak at various energies between 1 eV and 10 keV . Similar techniques have been developed by Eisen et al. for a personnel neutron dosimeter [7]. Unfortunately, a spectrometer which is based simply on boron shells and a 3 He counter, responds very weakly to neutrons with energies greater than about 100 eV . In order to enhance the spectrometer's response for neutron energies greater than about 100 eV, a paraffin jacket is placed around the 3 He counter . Then neutrons with energies greater than about 100 eV are moderated somewhat in the
detector detector detector detector detector detector detector
1 2 3 4 5 6 7
0
c
0
w O w U U r U
Neutron energy (eV) Fig. 2 . The set of response functions of the boron-shPsl spectrometer formed with the seven combinations of i° B loadings and paraffin thicknesses shown in table 1 .
C. K. Wang, T. E. Blue / A neutron spectrometer
paraffin, and thus have higher probabilities of being registered by the 3 He counter. The spherical 3 He counter is a product of LND Inc . The counter's response to thermal neutrons was calibrated with gold-foil activation in the thermal column of the Ohio State University Research Reactor. The calibration results show that the 3He gas pressure inside the counter is about 3.8 atm. Seven boron shells and three paraffin jackets were fabricated. The seven as-built combinations (which are referred to as detectors hereafter) of 1° B loadings in g/cm2 and paraffin jacket thicknesses in cm are provided in table 1. These shell jacket combinations were chosen so that their neutron response functions peak at nearly equally spaced intervals on a logarithmic energy scale for neutron energies ranging from 1 eV to 10 keV . The response functions for the seven detectors are shown in fig. 2. These response functions were calculated using the Monte Carlo code MORSE-CG [8] in conjunction with the BUGLE-80 multigroup cross-section library [9] . Because the response functions of the boron-shell spectrometer peak at nearly equally spaced intervals on a logarithmic energy scale for neutron energies ranging from 1 eV and 10 keV, neutron spectra (or histograms) can be obtained in this energy range by applying proper spectrum-unfolding codes to the measured data. 3. Spectrum unfolding The computer code used to unfold the neutron spectrum is a modified version of SPUNIT [10], which was originally written by Brackenbush et al. at Pacific Northwest Laboratory, for Bonner Sphere systems. The basic equation describing the unfolding problem is n
Ck
:=1
TiRik,
where Ck is the measured count rate for the k th detector, 0, is the neutron flux in the ith energy bin, R ik is the response function relating the response of the k th detector. to the neutron flux in the ith energy bin, and n is the total number of energy bins defining the neutron spectrum . The spectrum-unfolding technique used in SPUNIT is based on an iterative algorithm developed by Dc. ^Shenko et al . [111. This iterative technique is described by the following equation : m
~7 Rik
where
Ck Nk .l ,
2
the neutron flux for energy bin i calculated during the I th iteration ; m = the number of detectors ; Nk.1 = the calculated count rate for the k th detector for the l th iteration ; R i= l0i .l ik-
239
The iteration process is started with an assumed spectrum. As is shown in eq. (2), the fluxes for each iteration are calculated using the results of a previous iteration and the ratio of the measured and calculated detector count rate. The iteraticri is continued until either a specified number of iterations is exceeded or a specified convergence criterion is met. The convergence criterion is based on the deviation of the calculated detector count rate from the input detector count rate. This deviation is described by the equation e
m
m
k
1
(
( Nk .l _ Ck
2 ~~2
x 100` .
The modifications to SPUNIT which were made in order to apply it to the boron-shell spectrometer were to replace the original response matrix, which corresponds to a set of Bonner Spheres, with a response matrix which corresponds to the seven response functions described in fig . 2. Also, a spectrum-smoothing algorithm, suggested by Sanna [12], was incorporated into SPUNIT to reduce spectrum oscillation caused by ill-conditioned response matrices. A set of artificial inputs were created to test the performance of the modified SPUNIT code with the boron-shell spectrometer response function matrix . Each input contained seven detector counts (Ck, k =1-7) which were calculated according to eq. (1), using the 'ooron-shell spectrometer response function matrix elements R and assuming a monoenergetic neutron spectreirr! of 1-0-00 neutrons/ cm2 in the ith energy group. The intent was to find out how well unfolded neutron spectra would compare with monoenergetic input spectra . In BUGLE-80, the neutron energy range between 1 eV and 10 keV is subdivided into 12 energy groups. It was found that with a convergence criterion of e = 0.1%O, the SPUNIT code output spectra reproduced with 950 fidelity the monoenergetic spectra upon which the input Ck were based for monoenergetic input spectra in each of the 12 energy groups. That is, the unfolded spectra had about 950 neutrons/ cm2 in the input energy group, and only about 50 neutrons/ cm2 in the wrong energy groups . Fig. 3 illustrates the unfolded spectrum for a monoenergetic input spectrum with neutrons in energy group 7. The number of iterations which were required to reach the convergence criterion of e = 0.1% varied from 1800 to 92 300 depending on the input energy group. iiris number of iterations correspond 10 /- .D S- 1 .6 ruin of cpu time for an IBM mainframe computer . Increasing the number of iterations usually impro-ws the fidelity of unfolding . However, this improvement of fidelity quickly slows down, and levels off as the number of 1tGâ$r10T1S increases. The ultimate fidelity which can be achieved u determined by the characteristics of the spectrometer's response functions . In general, if a spectrometer has a set of response functions, each of
C. K. Wang, T. E. Blue / A neutron spectrometer
240
Beam Tube D 2 0 Moderator
N Eu m c 0 L
(20 cm x 36 .8 cm)
m c m u cd c 0 c
Neutron Spectrometer
m z
18 cm
Lithium Target
É
Fig. 4. The experimental setup for the neutron spectrum measurement, for neutrons emerging from a tank of D20. The centerline of the D20 tank and the neutron spectrometer are collinear with the centerline of the beam accelerator beam tube.
1000
u c m c
diameter and 20 cm in length. The tank wall is 0.32 cm thick, and is made of aluminum. The centerline of the D20 tank and the boron-shell spectrometer are collinear with the centerline of the accelerator beam tube .
400
0 43 z
200
or
0
1
2
1
~~ .
6 e 10 Neutron Energy Group Number 4
12
14
Fig. 3 . (a) A pseudo-monoenergetic neutron spectrum with neutron energy in group 7. This spectrum was used to generate the response (counts) of seven detectors using the detector response functions which are shown in fig. 2. (b) The spectrum obtained with the modified SPUNIT unfolding code using the set of counts generated by (a) as input.
5. Results and discussion The dotted line in fig. 5 represents the unfolded neutron spectrum, based on experimentally measured
07
which has a single peak, then the spectrometer gives good fidelity in unfolding. Also, in order to unfold a spectrum on a logarithmic energy scale, the peaks must span the energies of interest at nearly equally spaced intervals on such a scale.
â E
N E
V _
a E
c
4. Experiment The boron-shell spectrometer was used to measure the epithermal-neutron flux spectra in a test of a moderator assembly prototype for an accelerator-based neutron source for BNCT [131 . The test was carried out at the Ohio State University's Van de Graaff accelerator. Neutrons were generated by bombarding a 7 Li target with 2.5 MeV protons. The neutrons emitted from the 7 Li target are too energetic for BNCT, and therefore were moderated in the moderator assembly prototype (a tank of D20) . The experimental arrangement is shown in fig. 4. The D..O tank is cylindrical, and is 36 .5 cm in
r-~
Cn
r0 6 v
m
a
-----
MORSE results SPEC4 results SPUN IT resu!1s
-17
Q v z
..
05 10 0
..I 10 1
. .1 10 2 Neutron
. .. 10 3 Energy(eV)
..1 10 4
. .I 10 5
i ;.
i 10 6
Fig. 5. The calculated and the measured spectra of neutron emerging from the D,O moderator assembly.
C K Wang, TE. Blue / A neutron spectrometer
data . The left half of this spectrum (which is for neutron energies less than 10 keV) was unfolded from the data measured with the boron-shell spectrometer and is the important part of the spectrum for this paper. The right half of the spectrum is for neutron energies above 10 keV and is included for completeness. This part of the spectrum was unfolded using computer code SPEC-4 [14] with input data measured with a spherical protonrecoil proportional counter. Fig. 5 also includes as a solid line a neutron spectrum which was obtained from multi-group Monte Carlo calculations performed using MORSE-CG in conjunction with BUGLE-80 . As is shown, the measured spectrum based on the boron-shell spectrometer agrees quite well with the calculated spectrum. However, due to the uncertainties of the t° B loadings of the boron shells (and thus the uncertainties of the response functions), our boron-shell spectrometer should be further calibrated using a Scandium-filtered 2 keV neutron beam [15]. This paper has shown that the performance of our boron-shell spectrometer used in conjunction with a modified version of the SPUNIT code is quite good for neutrons in the energy region between 1 eV and 10 keV. This performance was verified by experiment and also numerically using a set of pseudo-monoenergetic neutron spectra. Acknowledgements This work was supported in part by the Nationz: Cancer Institute under grant 1 R01 CA47298-01 and by the 1.'S Department of Energy under contract DEAC02-76CH00016 . Special thanks go to Dr Jim Durham at Battelle Pacific Northwest Laboratory for providing the SPUNIT code.
241
References [1] H. Hatanaka, in : Boron-Neutron Capture Therapy for Tumors, ed . H. Hatanaka (Nishimura Co ., Ltd., 1986) p. 349. [2] R.G. Fairchild and V.P. Bond, Proc. First Int. Symp. on Neutron Capture Therapy, eds. G.L . Brownell and R.G . Fairchild, BNL-51730 (1983) p. 1. [3] D.J. Noonan, J.L . Russell and R.M . Brugger, Med. Phys. 13 (1986) 211. [4] R.M. Brugger et al ., Proc. Workshop on Neutron Capture Therapy, eds. R.G . Fairchild and V.P . Bond, BNL-51994 (1986) p. 32 . [5] F.J . Wheeler, Proc . Workshop on Neutron Capture Therapy, eds. R.G. Fairchild and V .P . Bond, BNL-51994 (1986) P. 92 . [6] C.K . Wang, T.E. Blue and R. Gahbauer, Nucl. Technol. 84 (1989) 93. [7] Y. Eisen et al ., Health Phys . 41 (1981) 349. [8] M.B . Emmett, ORNL-4972 (Oak Ridge National Laboratory, 1975). [9] R. Roussin, DLC-75 (Radiation Shielding Information Center, Oak Ridge National Laboratory, 1980) . [10] L.W . Brackenbush and R.I . Scherpelz, Proc . 17th Midyear Symp . of the Health Physics Society (1984) sections 4.14.6 . [11] J.J . Doroshenko et al., Nucl . Technol . 33 (1977) 296. [12] R.S . Sanna, HASL-311 (Health and Safety Laboratory, 1976). [13] C.K . Wang and T.E. Blue, in : Proc . Workshop on the Neutron Beam Development for Neutron Capture Therapy (Plenum Press, New York, 1989). [14] P.W . Benjamin, C.D . Kemshall and A. Brickstock, AWRE Report No. 09/68. [15] R.C. Greenwood and R.E . Chrien, Nucl . Instr. and Meth . 138 (1976) 125.
A NEUTRON SPECTROMETER FOR NEUTRONS WITH ENERGIES BETWEEN I eV AN
237
10 LeV
C.K. WANG * and T.E. BLUE
Ohio State University, Columbus, OH 43210, USA Received 30 Ocivber 1989
Epithermal neutrons with energies between 1 eV and 10 keV are of great interest in neutron capture therapy for treating deep-seated tumors. A new type of neutron spectrometer has been developed to measure neutron spectra :n this energy range. Conceptually, this new spectrometer is similar to the Bonner Sphere spectrometry system, in that it has a set of response functions which peak at various positions on the logarithmic energy scale. Therefore, by collecting a set of count rates, one can unfold the neutron spectrum. The performance of the spectrometer was tested in an experiment, and the associated unfolding technique was tested numerically. The results were satisfactory.
l. Introduction
Due to recent positive clinical results in Japan [1], research efforts in boron neutron capture therapy (BNCT) are regaining momentum . Among BNCT re= searchers, it is now the consensus [2] that epithermal neutron beams have advantages over thermal beams in treating deep-seated tumors, and large neutron fields have advantages over narrow neutron beams. Consequently, efforts are currently being made to extract large intense epithermal-neutron beams from nuclear reactors [3-5] and to create large intense epithermalneutron fields with accelerator-based neutron sources [6]. Radiobiological and neutronic studies have been performed which show that neutrons with energies between 1 eV and 10 keV are most suitable for treating deep-seated tumors. However, techniques for measuring epithermal-neutron spectra in large uncollimated neutron fields are not well developed. This paper describes the development and testing of a new type of neutron spectrometer for the measurement of epithermal-neutron spectra in large uncollimated neutron fields . This ribcS all Wp\rllili\ria1. nment in whiw vra ch paper 7Gr also l1G deJclaVG rllili\ria1. .m the u e muar neutron spectrum was measured for an accelerator-based neutron source for BNCT using this new spectrometer, and the measured spectrum is compared with the spectrum calculated with a Monte Carlo transport code .
* Present address: Kansas State University, Nuclear Engineering Department, Manhattan. KS 66502, USA.
2. Description of the neutron spectrometer The new neutron spectrometer is called a "boronshell spectrometer", and is similar in principle to a Bonner Sphere spectrometer. A Bonner Sphere spectrometer does not work well in this application, because: (1) it significantly modifies the neutron field at the beam port, and (2) its response functions do not show any peaks for neutron energies below 10 keV . The boron-shell spectrometer was developed to overcome these problems . As its name implies, the boron-shell spectrometer is based on a set of interchangeable hemispherical shells, which contain various amounts of '°B. A small (one inch in diameter) spherical 3 He proportional counter is a second component of the spectrometer. The proportional counter is located at the focus of the hemispherical shells (which will hereafter be called boron shells for convenience) . For the boron shells which contain larger amounts of '°B, the spectrometer has a third component, a spherical paraffin jacket which surrounds the 3He proportional counter. This jacket is matched to the boron shell, and is thicker for boron sheik which contain larger amounts of ' °B. Fig. 1 illustrates the geometric configuration of the boron-shell spectrometer. Arguments which support such a configuration are provided below : incoming neutrons are filtered by the spherical boron shell, before they reach the 3He counter. In its implementation the shell was made hemispherical, in order to conserve '°B. This was appropriate, since the neutron field which was
0168-9002/90/$03 .50 0 1990 - Elsevier Science Publishers B.V . (North-Holland)
C. K Wang, T.E. Blue/ A neutron spectrometer
238 Incident Neutrons
Void
-4
Boron Shell
{r-
1.25 cm
2.5 cm
Helium-3 Proportional Counter
Fig . 1 . The geometric configuration of the boron-shell neutron spectrometer.
measured was forwardly directed. Because the boron shell is spherical, neglecting scatter within the shell, the neutrons that strike the 3 He counter are restricted to those which are nearly perpendicularly incident upon the boron shell, and these neutrons pass through nearly 1°B the same thickness of in reaching the counter. Therefore, the filtering of spectra, and hence the response function of the spectrometer, depends only on the neutron energy (En ) and not on the neutron angular distribution . Since the neutron-capture cross section of 10B is proportional to En- 1/2, the boron shell filters out low-energy neutrons in preference to high-energy neu-
c
H
c
0 U
c
Table 1 As-built shell jacket compositions for the boron-shell neutron spectrometer Detector number
I° B loadings [g/cm2]
Paraffin thickness [cm]
1 2 3 4 5 6 7
0 .036 0 .067 0 .15 0 .39 0 .55 0 .79 0.95
0.0 0.0 0.64 0 .95 0 .95 0 .95 1 .27
trons . However, since the neutron-capture cross section for 3 He is also proportional to E. 1/2, the 3 He counter responds most strongly to the neutrons with the lowest energies . Therefore, by using a set of boron shells with various 1° Ii loadings and a 3 He counter, one can develop a set of response functions which peak at various energies between 1 eV and 10 keV . Similar techniques have been developed by Eisen et al. for a personnel neutron dosimeter [7]. Unfortunately, a spectrometer which is based simply on boron shells and a 3 He counter, responds very weakly to neutrons with energies greater than about 100 eV . In order to enhance the spectrometer's response for neutron energies greater than about 100 eV, a paraffin jacket is placed around the 3 He counter . Then neutrons with energies greater than about 100 eV are moderated somewhat in the
detector detector detector detector detector detector detector
1 2 3 4 5 6 7
0
c
0
w O w U U r U
Neutron energy (eV) Fig. 2 . The set of response functions of the boron-shPsl spectrometer formed with the seven combinations of i° B loadings and paraffin thicknesses shown in table 1 .
C. K. Wang, T. E. Blue / A neutron spectrometer
paraffin, and thus have higher probabilities of being registered by the 3 He counter. The spherical 3 He counter is a product of LND Inc . The counter's response to thermal neutrons was calibrated with gold-foil activation in the thermal column of the Ohio State University Research Reactor. The calibration results show that the 3He gas pressure inside the counter is about 3.8 atm. Seven boron shells and three paraffin jackets were fabricated. The seven as-built combinations (which are referred to as detectors hereafter) of 1° B loadings in g/cm2 and paraffin jacket thicknesses in cm are provided in table 1. These shell jacket combinations were chosen so that their neutron response functions peak at nearly equally spaced intervals on a logarithmic energy scale for neutron energies ranging from 1 eV to 10 keV . The response functions for the seven detectors are shown in fig. 2. These response functions were calculated using the Monte Carlo code MORSE-CG [8] in conjunction with the BUGLE-80 multigroup cross-section library [9] . Because the response functions of the boron-shell spectrometer peak at nearly equally spaced intervals on a logarithmic energy scale for neutron energies ranging from 1 eV and 10 keV, neutron spectra (or histograms) can be obtained in this energy range by applying proper spectrum-unfolding codes to the measured data. 3. Spectrum unfolding The computer code used to unfold the neutron spectrum is a modified version of SPUNIT [10], which was originally written by Brackenbush et al. at Pacific Northwest Laboratory, for Bonner Sphere systems. The basic equation describing the unfolding problem is n
Ck
:=1
TiRik,
where Ck is the measured count rate for the k th detector, 0, is the neutron flux in the ith energy bin, R ik is the response function relating the response of the k th detector. to the neutron flux in the ith energy bin, and n is the total number of energy bins defining the neutron spectrum . The spectrum-unfolding technique used in SPUNIT is based on an iterative algorithm developed by Dc. ^Shenko et al . [111. This iterative technique is described by the following equation : m
~7 Rik
where
Ck Nk .l ,
2
the neutron flux for energy bin i calculated during the I th iteration ; m = the number of detectors ; Nk.1 = the calculated count rate for the k th detector for the l th iteration ; R i= l0i .l ik-
239
The iteration process is started with an assumed spectrum. As is shown in eq. (2), the fluxes for each iteration are calculated using the results of a previous iteration and the ratio of the measured and calculated detector count rate. The iteraticri is continued until either a specified number of iterations is exceeded or a specified convergence criterion is met. The convergence criterion is based on the deviation of the calculated detector count rate from the input detector count rate. This deviation is described by the equation e
m
m
k
1
(
( Nk .l _ Ck
2 ~~2
x 100` .
The modifications to SPUNIT which were made in order to apply it to the boron-shell spectrometer were to replace the original response matrix, which corresponds to a set of Bonner Spheres, with a response matrix which corresponds to the seven response functions described in fig . 2. Also, a spectrum-smoothing algorithm, suggested by Sanna [12], was incorporated into SPUNIT to reduce spectrum oscillation caused by ill-conditioned response matrices. A set of artificial inputs were created to test the performance of the modified SPUNIT code with the boron-shell spectrometer response function matrix . Each input contained seven detector counts (Ck, k =1-7) which were calculated according to eq. (1), using the 'ooron-shell spectrometer response function matrix elements R and assuming a monoenergetic neutron spectreirr! of 1-0-00 neutrons/ cm2 in the ith energy group. The intent was to find out how well unfolded neutron spectra would compare with monoenergetic input spectra . In BUGLE-80, the neutron energy range between 1 eV and 10 keV is subdivided into 12 energy groups. It was found that with a convergence criterion of e = 0.1%O, the SPUNIT code output spectra reproduced with 950 fidelity the monoenergetic spectra upon which the input Ck were based for monoenergetic input spectra in each of the 12 energy groups. That is, the unfolded spectra had about 950 neutrons/ cm2 in the input energy group, and only about 50 neutrons/ cm2 in the wrong energy groups . Fig. 3 illustrates the unfolded spectrum for a monoenergetic input spectrum with neutrons in energy group 7. The number of iterations which were required to reach the convergence criterion of e = 0.1% varied from 1800 to 92 300 depending on the input energy group. iiris number of iterations correspond 10 /- .D S- 1 .6 ruin of cpu time for an IBM mainframe computer . Increasing the number of iterations usually impro-ws the fidelity of unfolding . However, this improvement of fidelity quickly slows down, and levels off as the number of 1tGâ$r10T1S increases. The ultimate fidelity which can be achieved u determined by the characteristics of the spectrometer's response functions . In general, if a spectrometer has a set of response functions, each of
C. K. Wang, T. E. Blue / A neutron spectrometer
240
Beam Tube D 2 0 Moderator
N Eu m c 0 L
(20 cm x 36 .8 cm)
m c m u cd c 0 c
Neutron Spectrometer
m z
18 cm
Lithium Target
É
Fig. 4. The experimental setup for the neutron spectrum measurement, for neutrons emerging from a tank of D20. The centerline of the D20 tank and the neutron spectrometer are collinear with the centerline of the beam accelerator beam tube.
1000
u c m c
diameter and 20 cm in length. The tank wall is 0.32 cm thick, and is made of aluminum. The centerline of the D20 tank and the boron-shell spectrometer are collinear with the centerline of the accelerator beam tube .
400
0 43 z
200
or
0
1
2
1
~~ .
6 e 10 Neutron Energy Group Number 4
12
14
Fig. 3 . (a) A pseudo-monoenergetic neutron spectrum with neutron energy in group 7. This spectrum was used to generate the response (counts) of seven detectors using the detector response functions which are shown in fig. 2. (b) The spectrum obtained with the modified SPUNIT unfolding code using the set of counts generated by (a) as input.
5. Results and discussion The dotted line in fig. 5 represents the unfolded neutron spectrum, based on experimentally measured
07
which has a single peak, then the spectrometer gives good fidelity in unfolding. Also, in order to unfold a spectrum on a logarithmic energy scale, the peaks must span the energies of interest at nearly equally spaced intervals on such a scale.
â E
N E
V _
a E
c
4. Experiment The boron-shell spectrometer was used to measure the epithermal-neutron flux spectra in a test of a moderator assembly prototype for an accelerator-based neutron source for BNCT [131 . The test was carried out at the Ohio State University's Van de Graaff accelerator. Neutrons were generated by bombarding a 7 Li target with 2.5 MeV protons. The neutrons emitted from the 7 Li target are too energetic for BNCT, and therefore were moderated in the moderator assembly prototype (a tank of D20) . The experimental arrangement is shown in fig. 4. The D..O tank is cylindrical, and is 36 .5 cm in
r-~
Cn
r0 6 v
m
a
-----
MORSE results SPEC4 results SPUN IT resu!1s
-17
Q v z
..
05 10 0
..I 10 1
. .1 10 2 Neutron
. .. 10 3 Energy(eV)
..1 10 4
. .I 10 5
i ;.
i 10 6
Fig. 5. The calculated and the measured spectra of neutron emerging from the D,O moderator assembly.
C K Wang, TE. Blue / A neutron spectrometer
data . The left half of this spectrum (which is for neutron energies less than 10 keV) was unfolded from the data measured with the boron-shell spectrometer and is the important part of the spectrum for this paper. The right half of the spectrum is for neutron energies above 10 keV and is included for completeness. This part of the spectrum was unfolded using computer code SPEC-4 [14] with input data measured with a spherical protonrecoil proportional counter. Fig. 5 also includes as a solid line a neutron spectrum which was obtained from multi-group Monte Carlo calculations performed using MORSE-CG in conjunction with BUGLE-80 . As is shown, the measured spectrum based on the boron-shell spectrometer agrees quite well with the calculated spectrum. However, due to the uncertainties of the t° B loadings of the boron shells (and thus the uncertainties of the response functions), our boron-shell spectrometer should be further calibrated using a Scandium-filtered 2 keV neutron beam [15]. This paper has shown that the performance of our boron-shell spectrometer used in conjunction with a modified version of the SPUNIT code is quite good for neutrons in the energy region between 1 eV and 10 keV. This performance was verified by experiment and also numerically using a set of pseudo-monoenergetic neutron spectra. Acknowledgements This work was supported in part by the Nationz: Cancer Institute under grant 1 R01 CA47298-01 and by the 1.'S Department of Energy under contract DEAC02-76CH00016 . Special thanks go to Dr Jim Durham at Battelle Pacific Northwest Laboratory for providing the SPUNIT code.
241
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